Geometry of the Unit Sphere in Polynomial Spaces

by Jesús Ferrer, Domingo García, Manuel Maestre, Gustavo A. Muñoz, Daniel L. Rodríguez, Juan B. Seoane

2023 · Springer Nature

This brief presents a global perspective on the geometry of spaces of polynomials. Its particular focus is on polynomial spaces of dimension 3, providing, in that case, a graphical representation of the unit ball. Also, the extreme points in the unit ball of several polynomial spaces are characterized. Finally, a number of applications to obtain sharp classical polynomial inequalities are presented. The study performed is the first ever complete account on the geometry of the unit ball of polynomial spaces. Nowadays there are hundreds of research papers on this topic and our work gathers the state of the art of the main and/or relevant results up to now. This book is intended for a broad audience, including undergraduate and graduate students, junior and senior researchers and it also serves as a source book for consultation. In addition to that, we made this work visually attractive by including in it over 50 original figures in order to help in the understanding of all the results and techniques included in the book.

Convex Analysis in Polynomial Spaces with Applications

by Domingo García, Mingu Jung, Manuel Maestre, Gustavo A. Muñoz Fernández, Juan B. Seoane Sepúlveda

2025 · CRC Press

Convex Analysis in Polynomial Spaces with Applications is intended to serve a broad audience of undergraduate and graduate students, junior and senior researchers, and as a general self-study guide for anyone who wishes to get acquainted with geometry of Banach spaces of polynomials with applications. This text is specifically designed to be appealing and accessible to the reader, and provides a general overview on the topic together with new and interesting directions of research. The text also contains original results and material never published before. Features · Comprehensive review on the geometry of spaces of polynomials. · Visually attractive and accessible presentation, with over 75 explanatory figures. · Contains many examples illustrating the results and techniques appearing in the book. · Open (and deep!) questions within the area are provided so that the interested reader can begin doing independent research using the techniques presented in the text. · It also features original results by the authors.